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            <small>
              <a href="#Procedure">Procedure<br></a>
              <a href="#Abstract">Abstract<br></a>
              <a href="#Required_Reading">Required_Reading<br></a>
              <a href="#Keywords">Keywords<br></a>
              <a href="#Brief_I/O">Brief_I/O<br></a>
              <a href="#Detailed_Input">Detailed_Input<br></a>

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              <small>               <a href="#Detailed_Output">Detailed_Output<br></a>
              <a href="#Parameters">Parameters<br></a>
              <a href="#Exceptions">Exceptions<br></a>
              <a href="#Files">Files<br></a>
              <a href="#Particulars">Particulars<br></a>
              <a href="#Examples">Examples<br></a>

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              <small>               <a href="#Restrictions">Restrictions<br></a>
              <a href="#Literature_References">Literature_References<br></a>
              <a href="#Author_and_Institution">Author_and_Institution<br></a>
              <a href="#Version">Version<br></a>
              <a href="#Index_Entries">Index_Entries<br></a>
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<h4><a name="Procedure">Procedure</a></h4>
<PRE>
   void invort_c ( ConstSpiceDouble   m  [3][3],
                   SpiceDouble        mit[3][3] ) 

</PRE>
<h4><a name="Abstract">Abstract</a></h4>
<PRE>
 
   Given a matrix, construct the matrix whose rows are the  
   columns of the first divided by the length squared of the 
   the corresponding columns of the input matrix. 
 </PRE>
<h4><a name="Required_Reading">Required_Reading</a></h4>
<PRE>
 
   None. 
 </PRE>
<h4><a name="Keywords">Keywords</a></h4>
<PRE>
 
   MATRIX 
 

</PRE>
<h4><a name="Brief_I/O">Brief_I/O</a></h4>
<PRE>
 
   Variable  I/O  Description 
   --------  ---  -------------------------------------------------- 
   m          I   A 3x3 matrix. 
   mit        I   m after transposition and scaling of rows. 
    </PRE>
<h4><a name="Detailed_Input">Detailed_Input</a></h4>
<PRE>
 
   m          is a 3x3 matrix. 
 </PRE>
<h4><a name="Detailed_Output">Detailed_Output</a></h4>
<PRE>
 
   mit        is the matrix obtained by transposing m and dividing 
              the rows by squares of their norms. 
 </PRE>
<h4><a name="Parameters">Parameters</a></h4>
<PRE>
 
   None. 
 </PRE>
<h4><a name="Exceptions">Exceptions</a></h4>
<PRE>
 
   1) If any of the columns of m have zero length, the error  
      SPICE(ZEROLENGTHCOLUMN) will be signaled. 
       
   2) If any column is too short to allow computation of the 
      reciprocal of its length without causing a floating  
      point overflow, the error SPICE(COLUMNTOOSMALL) will 
      be signalled. 
       </PRE>
<h4><a name="Files">Files</a></h4>
<PRE>
 
   None. 
 </PRE>
<h4><a name="Particulars">Particulars</a></h4>
<PRE>
 
   Suppose that m is the matrix  
     
           -                      - 
          |   A*u    B*v     C*w   |    
          |      1      1       1  | 
          |                        | 
          |   A*u    B*v     C*w   |    
          |      2      2       2  | 
          |                        | 
          |   A*u    B*v     C*w   |   
          |      3      3       3  | 
           -                      - 
 
   where the vectors (u , u , u ),  (v , v , v ),  and (w , w , w ) 
                       1   2   3      1   2   3          1   2   3 

   are unit vectors. This routine produces the matrix: 
     
     
           -                      - 
          |   a*u    a*u     a*u   |    
          |      1      2       3  | 
          |                        | 
          |   b*v    b*v     b*v   |    
          |      1      2       3  | 
          |                        | 
          |   c*w    c*w     c*w   |   
          |      1      2       3  | 
           -                      - 
     
   where a = 1/A, b = 1/B, and c = 1/C. 
     </PRE>
<h4><a name="Examples">Examples</a></h4>
<PRE>
 
   Suppose that you have a matrix m whose columns are orthogonal  
   and have non-zero norm (but not necessarily norm 1).  Then the  
   routine <b>invort_c</b> can be used to construct the inverse of m: 
      
      #include &quot;SpiceUsr.h&quot;
           .
           .
           .
      <b>invort_c</b> ( m, invers );
         
   This method is numerically more robust than calling the 
   routine <a href="invert_c.html">invert_c</a>. 
 </PRE>
<h4><a name="Restrictions">Restrictions</a></h4>
<PRE>
 
   None. 
 </PRE>
<h4><a name="Literature_References">Literature_References</a></h4>
<PRE>
 
   None. 
 </PRE>
<h4><a name="Author_and_Institution">Author_and_Institution</a></h4>
<PRE>
 
   W.L. Taber     (JPL) 
   N.J. Bachman   (JPL)
</PRE>
<h4><a name="Version">Version</a></h4>
<PRE>
 
   -CSPICE Version 1.0.0, 02-JAN-2002 (WLT) (NJB)
</PRE>
<h4><a name="Index_Entries">Index_Entries</a></h4>
<PRE>
 
   Transpose a matrix and invert the lengths of the rows 
   Invert a pseudo orthogonal matrix
 </PRE>
<h4>Link to routine invort_c source file <a href='../../../src/cspice/invort_c.c'>invort_c.c</a> </h4>

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   <pre>Wed Jun  9 13:05:25 2010</pre>

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